STABILITY ANALYSIS OF DRUG ABUSE TRANSMISSION DYNAMICS

Authors

  • Abqorry Zakiyyah Andalas University
  • Susila Bahri Andalas University

DOI:

https://doi.org/10.25077/jmua.14.1.103-116.2025

Keywords:

Mathematical Modelling, Drug Abuse Transmission, SLARS Model

Abstract

This research introduced a nonlinear deterministic model known as SLARS (Susceptible, Light Users, Addicted, and Reformed Users) along with a stability analysis to investigate the dynamics of drug abuse transmission. The basic reproduction number (R0) was calculated using the next-generation matrix method. Following this, the study examined the local stability of both the drug abuse-free and endemic equilibrium points. The findings indicated that when R0 is below 1, the drug abuse-free equilibrium point is locally stable. In contrast, when R0 is greater than 1, the endemic equilibrium point shows local stability. Additionally, simulation results supported the analytical conclusions of the study.

References

J. Ahmad, U.C. Joel, F.O. Talabi, O.N. Bibian, A.B. Aiyesimoju, V.O. Adefemi, V.C. Gever, textit{Impact of social media-based intervention in reducing youths’ propensity to engage in drug abuse in Nigeria}, Evaluation and program planning, textbf{94} (2022), 102--122.

J.R. Branan, E. William, textit{Differential Equations: An Introduction to Modern Methods and Aplication}, Wiley, New York, 2015.

O. Diekmann, J.A.P. Heesterbeek, M.G. Roberts, textit{The construction of next generation matrices for compartmental epidemic models}, J. R.Soc. Interface. textbf{7} (2010), 873--885.

L. Edelstein-Keshet,textit{Mathematical Models in Biology}, Random House, New York, 2008.

R. L. Evans, N.O. JoAnn, textit{COVID-19 Pandemic: World in Turmoil}, Train Education, California, 2022.

Herindrasti, V.L. Sinta, textit{Drug-free ASEAN 2025: Challenges for Indonesia in Combating Drug Abuse}, International Relations Journal, textbf{7(1)} (2018), 19--33.

I. Kabbash, O. Zidan, S. Saied, textit{ Substance abuse among university students in Egypt: Prevalence and correlates}, Eastern Mediterranean Health Journal, textbf{28(1)}(2022), 31--40

W.G. Kelley, A.C. Peterson, textit{The Theory of Differential Equations Classical and Qualitative Second Edition}, Springer, New York, 2010.

Imron, Masyhuri et al, textit{2019 Drug Abuse Prevalence Survey}, National Narcotics Board, Jakarta, 2020.

B.P. Machhi, J.E Magar, S.S. Mishra, K.A. Salauddin, K.R. Manawarali, M.L.K.A. Vyas, textit{Review on current increases of drug abuse among teenagers}, Research Chronicler, textbf{10(2)} (2022), 58--71.

S. Mushayabasa and G. Tapedzesa, textit{Modeling illicit drug use dynamics and its optimal control analysis}, Computational and Mathematical Methods in medicine, (2015), https://dx.doi.org/10.1155/2015/383154.

National Institute on Drug Abuse, {it Drugs, brain, and behavior: the science of addiction}, (3rd edition), National Institute on Drug Abuse National Institutes of Health, Rockville MD, 2007.

National Narcotics Board of Republic of Indonesia, textit{Indonesia Drugs Report 2022}, National Narcotics Board, Jakarta, 2022.

B. Susila, F. Indah, N. Hamidah, L. Riri, F. Lili, textit{Analysis of the effects of foreign travelers and immigrants on omicron transmission in Indonesia}, International Journal of Mathematics and Computer Science, textbf{19} (2024), 893-902.

L, Stephen, textit{Dynamical system with application using mathematics}, Birkhauser, Boston, 2017.

BPS-Statistics Indonesia, textit{Statistical Yearbook of Indonesia}, BPS-Statistics Indonesia, Jakarta, 2022.

E. White and C. Comiskey, textit{Heroin epidemics, treatment and ode modeling}, Mathematical Biosciences, textbf{208} (2007), 312 -- 324.

Our editor speaking at the PKP conference.

Downloads

Published

31-01-2025

Issue

Vol. 14 No. 1 (2025)

Section

Articles

License

All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.

Copyright Holder

The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.

Author Rights

While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:

  • Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
  • Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.

Creative Commons License (CC BY-SA)

Under the terms of the CC BY-SA license, users are free to:

  • Share: Copy and redistribute the material in any medium or format.
  • Adapt: Remix, transform, and build upon the material for any purpose, even commercially.

However, the following conditions apply:

  • Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
  • ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.

For more information about the CC BY-SA license, please visit the Creative Commons website.

Third-Party Content

If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.

Copyright and Licensing Information Display

The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.

No "All Rights Reserved"

As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.

Â